The Union of Soldiers' Mothers Committees intends to meet with Akhmad Zakayev, a representative for Chechen rebel leader Aslan Maskhadov, to discuss proposals for ending the five-year-old war between Russia and Chechen separatists.
Moscow has refused to negotiate with Chechen rebels, describing them as terrorists, and has not endorsed the meeting which will have no official weight.
The talks would be "basically justifying those who encourage and carry out terrorist attacks," Foreign Minister Sergey Lavrov said on Tuesday.
Top pro-Moscow Chechen officials also criticised the planned talks, saying terrorists should not be negotiated with.
"Talks with Maskhadov and his people must be conducted by prosecutors, not by public organisations," said Chechen State Council Chairman Taus Dzhabrailov, according to the Interfax news agency.
But the meeting, which is being organised by Belgian European Parliament member Bart Staes, comes two days before President Vladimir Putin's summit with the European Union in the Netherlands and could renew international attention on the region.
Western criticism of Russian abuses in Chechnya and calls for it to seek a political solution were strong in the early years of the conflict, but have faded amid rhetoric about terrorism.
The Kremlin casts the war in the predominantly Muslim republic as part of the fight against global terrorism and claims that the rebels get significant aid and some fighters from abroad.
"Together with the Chechen rebel side we will discuss what steps to take in order to end the war in Chechnya"
The Union of Soldiers' Mothers Committees
On the other hand, the rebels say they are conducting a legitmate struggle for self-determination in the face of Moscow's genocidal policies in the region.
Valentina Melnikova, head of the soldiers' mothers group, said the meeting was an effort "to find a way out of the Chechen impasse".
"Together with the Chechen rebel side we will discuss what steps to take in order to end the war in Chechnya," she told The Associated Press.
The group rose to prominence in the 1994-96 Chechen war, calling for a withdrawal from Chechnya and an improvement in the dismal conditions within the Russian army.
Maskhadov, whom Zakayev represents, was president of Chechnya during its period of de-facto independence between 1996 and 1999.
Russian forces are accused of
widespread abuses in Chechnya
Russian forces pulled out of Chechnya in 1996 after a 20-month war against separatists ended in a stalemate.
Russian forces resumed fighting there in 1999, and the then elected president Maskhadov's whereabouts have been unknown since then.